Assuming a random sample of ???? pairs has been selected and the distribution of the differences is approximately normal, use a ????-test to perform each of the following hypothesis tests. In particular, include the rejection region, the value of ????obs, the decision concerning ????0, and the approximate ????-value associated with ????obs.

(a) Test ????0 ∶ ???????? ≥ ???????? when ???? = 0.05, ???? = 30, ????̄ = −35.5, and ???????? = 27.6.

(b) Test ????0 ∶ ???????? ≤ ???????? when ???? = 0.01, ???? = 18, ????̄ = 5.2, and ???????? = 8.9.

(c) Test ????0 ∶ ???????? ≤ ???????? when ???? = 0.05, ???? = 61, ????̄ = 22.5, and ???????? = 104.1.

(d) Test ????0 ∶ ???????? ≥ ???????? when ???? = 0.01, ???? = 121, ????̄ = 3.1, and ???????? = 15.2.

(e) Test ????0 ∶ ???????? = ???????? when ???? = 0.01, ???? = 75, ????̄ = 13.3, and ???????? = 4.7.